You can browse or search the archive via the Archive page. The channels list on the right show the channels available. You can search via the form on the top left, or if you are on a mobile device, opening the menu.
Greyed out channels are archived channels in Slack itself. You can still read the messages in there of course, but accessing it or posting new messages has been limited on Slack itself.
On the archive page, you can search for keywords and limit your results to a certain channel or user if you need to.